检查第M个斐波那契数是否除以第N个斐波那契数

给定两个数字M和N，任务是检查第M个和第N个斐波纳契数是否彼此完全除。
例子：

Input: M = 3, N = 6 
Output: Yes 
F(3) = 2, F(6) = 8 and F(6) % F(3) = 0 
Input: M = 2, N = 9 
Output: No

天真的方法是找到第N个和第M个斐波那契数，并检查它们是否被完全整除。
一种有效的方法是使用Fibonacci属性确定结果。如果m完美地除以n，则F _m也可以完美地除以F _n ，否则就不会。
例外：当N为2时，因为Fibo ₂为1总是可能的，这将除以其他斐波那契数。
下面是上述方法的实现：

C++

// C++ program to check if
// M-th fibonacci divides N-th fibonacci
#include 
using namespace std;
 
void check(int n, int m)
{
    // exceptional case for F(2)
    if (n == 2 || m == 2 || n % m == 0) {
        cout << "Yes" << endl;
    }
    // if none of the above cases,
    // hence not divisible
    else {
        cout << "No" << endl;
    }
}
 
// Driver Code
int main()
{
    int m = 3, n = 9;
    check(n, m);
 
    return 0;
}

Java

// Java program to check
// if M-th fibonacci
// divides N-th fibonacci
import java.io.*;
 
class GFG
{
static void check(int n, int m)
{
    // exceptional case for F(2)
    if (n == 2 || m == 2 ||
        n % m == 0)
    {
        System.out.println( "Yes");
    }
     
    // if none of the above cases,
    // hence not divisible
    else
    {
        System.out.println( "No");
    }
}
 
// Driver Code
public static void main (String[] args)
{
    int m = 3, n = 9;
    check(n, m);
}
}
 
// This code is contributed
// by anuj_67.

Python 3

# Python 3 program to
# check if M-th fibonacci
# divides N-th fibonacci
 
def check(n, m):
 
    # exceptional case for F(2)
    if (n == 2 or m == 2 or
        n % m == 0) :
        print( "Yes" )
     
    # if none of the above
    # cases, hence not divisible
    else :
        print( "No" )
 
# Driver Code
m = 3
n = 9
check(n, m)
 
# This code is contributed
# by Smitha

C#

// C# program to check
// if M-th fibonacci
// divides N-th fibonacci
using System;
 
class GFG
{
static void check(int n, int m)
{
    // exceptional case for F(2)
    if (n == 2 || m == 2 ||
        n % m == 0)
    {
         Console.WriteLine( "Yes");
    }
     
    // if none of the above cases,
    // hence not divisible
    else
    {
        Console.WriteLine( "No");
    }
}
 
// Driver Code
public static void Main ()
{
    int m = 3, n = 9;
    check(n, m);
}
}
 
// This code is contributed
// by anuj_67.

Javascript

 
// Javascript program to check if
// M-th fibonacci divides N-th fibonacci
 
function check(n, m)
{
    // exceptional case for F(2)
    if (n == 2 || m == 2 || n % m == 0) {
        document.write("Yes" + "<br>");
    }
    // if none of the above cases,
    // hence not divisible
    else {
        document.write("No" + "<br>");
    }
}
 
// Driver Code
  
    let m = 3, n = 9;
    check(n, m);
 
// This code is contributed by Mayank Tyagi
 

输出：

Yes

时间复杂度： O(1)。